Index

_

__init__() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method) (hpfracc.algorithms.advanced_methods.HadamardDerivative method) (hpfracc.algorithms.advanced_methods.MarchaudDerivative method) (hpfracc.algorithms.advanced_methods.ParallelAdomianDecomposition method) (hpfracc.algorithms.advanced_methods.ParallelHadamardDerivative method) (hpfracc.algorithms.advanced_methods.ParallelMarchaudDerivative method) (hpfracc.algorithms.advanced_methods.ParallelReizFellerDerivative method) (hpfracc.algorithms.advanced_methods.ParallelWeylDerivative method) (hpfracc.algorithms.advanced_methods.ReizFellerDerivative method) (hpfracc.algorithms.advanced_methods.WeylDerivative method) (hpfracc.algorithms.derivatives.RiemannLiouville method) (hpfracc.algorithms.derivatives.UnifiedFractionalOperator method) (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalLaplacian method) (hpfracc.algorithms.fractional_operator_methods.FractionalMellinTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalZTransform method) (hpfracc.algorithms.fractional_operator_methods.SpecialMethodsConfig method) (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedMarchaudDerivative method) (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedReizFellerDerivative method) (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedWeylDerivative method) (hpfracc.algorithms.fractional_operator_methods.UnifiedSpecialMethods method) (hpfracc.algorithms.integral_methods.CaputoIntegral method) (hpfracc.algorithms.integral_methods.RiemannLiouvilleIntegral method) (hpfracc.algorithms.integral_methods.WeylIntegral method) (hpfracc.algorithms.optimized_methods.AdvancedFFTMethods method) (hpfracc.algorithms.optimized_methods.GPUConfig method) (hpfracc.algorithms.optimized_methods.GPUOptimizedCaputo method) (hpfracc.algorithms.optimized_methods.GPUOptimizedGrunwaldLetnikov method) (hpfracc.algorithms.optimized_methods.GPUOptimizedMethods method) (hpfracc.algorithms.optimized_methods.GPUOptimizedRiemannLiouville method) (hpfracc.algorithms.optimized_methods.L1L2Schemes method) (hpfracc.algorithms.optimized_methods.MultiGPUManager method) (hpfracc.algorithms.optimized_methods.NumbaFractionalKernels method) (hpfracc.algorithms.optimized_methods.NumbaOptimizer method) (hpfracc.algorithms.optimized_methods.NumbaParallelManager method) (hpfracc.algorithms.optimized_methods.ParallelConfig method) (hpfracc.AtanganaBaleanuDerivative method) (hpfracc.CaputoDerivative method) (hpfracc.CaputoFabrizioDerivative method) (hpfracc.CaputoIntegral method) (hpfracc.core.derivatives.BaseFractionalDerivative method) (hpfracc.core.derivatives.FractionalDerivativeChain method) (hpfracc.core.derivatives.FractionalDerivativeFactory method) (hpfracc.core.derivatives.FractionalDerivativeOperator method) (hpfracc.core.fractional_implementations._AlphaCompatibilityWrapper method) (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method) (hpfracc.core.fractional_implementations.AtanganaBaleanuDerivative method) (hpfracc.core.fractional_implementations.CaputoDerivative method) (hpfracc.core.fractional_implementations.CaputoFabrizioDerivative method) (hpfracc.core.fractional_implementations.FractionalFourierTransform method) (hpfracc.core.fractional_implementations.FractionalLaplacian method) (hpfracc.core.fractional_implementations.GrunwaldLetnikovDerivative method) (hpfracc.core.fractional_implementations.HadamardDerivative method) (hpfracc.core.fractional_implementations.MarchaudDerivative method) (hpfracc.core.fractional_implementations.MillerRossDerivative method) (hpfracc.core.fractional_implementations.ReizFellerDerivative method) (hpfracc.core.fractional_implementations.RiemannLiouvilleDerivative method) (hpfracc.core.fractional_implementations.RieszFisherOperator method) (hpfracc.core.fractional_implementations.WeylDerivative method) (hpfracc.core.integrals.CaputoIntegral method) (hpfracc.core.integrals.FractionalIntegral method) (hpfracc.core.integrals.FractionalIntegralFactory method) (hpfracc.core.integrals.HadamardIntegral method) (hpfracc.core.integrals.MarchaudIntegral method) (hpfracc.core.integrals.MillerRossIntegral method) (hpfracc.core.integrals.RiemannLiouvilleIntegral method) (hpfracc.core.integrals.WeylIntegral method) (hpfracc.FractionalFourierTransform method) (hpfracc.FractionalLaplacian method) (hpfracc.FractionalMellinTransform method) (hpfracc.FractionalOrder method) (hpfracc.FractionalZTransform method) (hpfracc.GrunwaldLetnikovDerivative method) (hpfracc.HadamardDerivative method) (hpfracc.MarchaudDerivative method) (hpfracc.ml.backends.BackendManager method) (hpfracc.ml.core.FractionalAttention method) (hpfracc.ml.core.FractionalAutoML method) (hpfracc.ml.core.FractionalLossFunction method) (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.core.MLConfig method) (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method) (hpfracc.ml.gnn_layers.FractionalGraphAttention method) (hpfracc.ml.gnn_layers.FractionalGraphPooling method) (hpfracc.ml.gnn_models.BaseFractionalGNN method) (hpfracc.ml.gnn_models.FractionalGAT method) (hpfracc.ml.gnn_models.FractionalGraphSAGE method) (hpfracc.ml.gnn_models.FractionalGraphUNet method) (hpfracc.ml.gpu_optimization.AMPFractionalEngine method) (hpfracc.ml.gpu_optimization.ChunkedFFT method) (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method) (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method) (hpfracc.ml.gpu_optimization.GPUProfiler method) (hpfracc.ml.gpu_optimization.PerformanceMetrics method) (hpfracc.ml.layers.BackendManager method) (hpfracc.ml.layers.FractionalBatchNorm1d method) (hpfracc.ml.layers.FractionalConv1D method) (hpfracc.ml.layers.FractionalConv2D method) (hpfracc.ml.layers.FractionalDropout method) (hpfracc.ml.layers.FractionalLayerBase method) (hpfracc.ml.layers.FractionalLayerNorm method) (hpfracc.ml.layers.FractionalLinear method) (hpfracc.ml.layers.FractionalLSTM method) (hpfracc.ml.layers.FractionalMaxUnpool1d method) (hpfracc.ml.layers.FractionalMaxUnpool2d method) (hpfracc.ml.layers.FractionalMaxUnpool3d method) (hpfracc.ml.layers.FractionalOps method) (hpfracc.ml.layers.FractionalPooling method) (hpfracc.ml.layers.FractionalSelfAttention method) (hpfracc.ml.layers.FractionalTransformer method) (hpfracc.ml.layers.LayerConfig method) (hpfracc.ml.losses.FractionalBCELoss method) (hpfracc.ml.losses.FractionalCombinedLoss method) (hpfracc.ml.losses.FractionalCosineEmbeddingLoss method) (hpfracc.ml.losses.FractionalCrossEntropyLoss method) (hpfracc.ml.losses.FractionalCTCLoss method) (hpfracc.ml.losses.FractionalCustomLoss method) (hpfracc.ml.losses.FractionalHuberLoss method) (hpfracc.ml.losses.FractionalKLDivergenceLoss method) (hpfracc.ml.losses.FractionalKLDivLoss method) (hpfracc.ml.losses.FractionalLossFunction method) (hpfracc.ml.losses.FractionalMarginRankingLoss method) (hpfracc.ml.losses.FractionalMomentMatchingLoss method) (hpfracc.ml.losses.FractionalMSELoss method) (hpfracc.ml.losses.FractionalMultiMarginLoss method) (hpfracc.ml.losses.FractionalNLLLoss method) (hpfracc.ml.losses.FractionalPathwiseLoss method) (hpfracc.ml.losses.FractionalPoissonNLLLoss method) (hpfracc.ml.losses.FractionalSDEMSELoss method) (hpfracc.ml.losses.FractionalSmoothL1Loss method) (hpfracc.ml.losses.FractionalTripletMarginLoss method) (hpfracc.ml.optimized_optimizers.FractionalOptimizer method) (hpfracc.ml.optimized_optimizers.OptimizedFractionalAdam method) (hpfracc.ml.optimized_optimizers.OptimizedFractionalRMSprop method) (hpfracc.ml.optimized_optimizers.OptimizedFractionalSGD method) (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method) (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalOrder method) (hpfracc.ml.spectral_autograd.BoundedAlphaParameter method) (hpfracc.ml.spectral_autograd.SpectralFractionalDerivative method) (hpfracc.ml.spectral_autograd.SpectralFractionalFunction method) (hpfracc.ml.spectral_autograd.SpectralFractionalLayer method) (hpfracc.ml.spectral_autograd.SpectralFractionalNetwork method) (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method) (hpfracc.ml.stochastic_memory_sampling.ImportanceSampler method) (hpfracc.ml.stochastic_memory_sampling.StochasticFractionalLayer method) (hpfracc.ml.stochastic_memory_sampling.StochasticMemorySampler method) (hpfracc.ml.stochastic_memory_sampling.StratifiedSampler method) (hpfracc.ml.variance_aware_training.AdaptiveSamplingManager method) (hpfracc.ml.variance_aware_training.StochasticSeedManager method) (hpfracc.ml.variance_aware_training.VarianceAwareCallback method) (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method) (hpfracc.ml.variance_aware_training.VarianceMetrics method) (hpfracc.ml.variance_aware_training.VarianceMonitor method) (hpfracc.ReizFellerDerivative method) (hpfracc.RiemannLiouvilleDerivative method) (hpfracc.RiemannLiouvilleIntegral method) (hpfracc.WeylDerivative method)

_adaptive_fft_direct_relative_l2() (in module hpfracc.algorithms.integral_methods) _AlphaCompatibilityWrapper (class in hpfracc.core.fractional_implementations) _analytical_method() (hpfracc.algorithms.fractional_operator_methods.FractionalMellinTransform method) (hpfracc.FractionalMellinTransform method) _apply_activation() (hpfracc.ml.core.FractionalNeuralNetwork method) _apply_fractional_gradients() (hpfracc.ml.optimized_optimizers.FractionalOptimizer method) _auto_select_method() (hpfracc.algorithms.fractional_operator_methods.UnifiedSpecialMethods method) _build_network() (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_models.BaseFractionalGNN method) (hpfracc.ml.gnn_models.FractionalGAT method) (hpfracc.ml.gnn_models.FractionalGCN method) (hpfracc.ml.gnn_models.FractionalGraphSAGE method) (hpfracc.ml.gnn_models.FractionalGraphUNet method) _check_variance() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method) _chirp_based_method() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.FractionalFourierTransform method) _coerce_function() (hpfracc.CaputoIntegral method) (hpfracc.core.integrals.CaputoIntegral method) (hpfracc.core.integrals.MillerRossIntegral method) (hpfracc.core.integrals.RiemannLiouvilleIntegral method) (hpfracc.core.integrals.WeylIntegral method) (hpfracc.RiemannLiouvilleIntegral method) _compute_adaptive() (hpfracc.algorithms.integral_methods.RiemannLiouvilleIntegral method) _compute_adomian_polynomial() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method) _compute_array_numpy() (hpfracc.core.integrals.HadamardIntegral method) (hpfracc.core.integrals.MarchaudIntegral method) (hpfracc.core.integrals.MillerRossIntegral method) (hpfracc.core.integrals.RiemannLiouvilleIntegral method) (hpfracc.core.integrals.WeylIntegral method) (hpfracc.RiemannLiouvilleIntegral method) _compute_array_torch() (hpfracc.core.integrals.HadamardIntegral method) (hpfracc.core.integrals.MarchaudIntegral method) (hpfracc.core.integrals.MillerRossIntegral method) (hpfracc.core.integrals.RiemannLiouvilleIntegral method) (hpfracc.core.integrals.WeylIntegral method) (hpfracc.RiemannLiouvilleIntegral method) _compute_direct() (hpfracc.algorithms.integral_methods.RiemannLiouvilleIntegral method) _compute_direct_discrete_legacy() (hpfracc.algorithms.integral_methods.RiemannLiouvilleIntegral method) _compute_fft() (hpfracc.algorithms.integral_methods.RiemannLiouvilleIntegral method) _compute_frft() (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedWeylDerivative method) _compute_hadamard() (hpfracc.algorithms.advanced_methods.HadamardDerivative method) (hpfracc.HadamardDerivative method) _compute_hybrid() (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedWeylDerivative method) _compute_integral_term() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method) _compute_laplacian() (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedReizFellerDerivative method) _compute_marchaud_segment() (hpfracc.algorithms.advanced_methods.MarchaudDerivative method) (hpfracc.MarchaudDerivative method) _compute_memory_optimized() (hpfracc.algorithms.advanced_methods.MarchaudDerivative method) (hpfracc.MarchaudDerivative method) _compute_moment() (hpfracc.ml.losses.FractionalMomentMatchingLoss method) _compute_parallel() (hpfracc.algorithms.advanced_methods.WeylDerivative method) (hpfracc.WeylDerivative method) _compute_scalar() (hpfracc.core.integrals.HadamardIntegral method) (hpfracc.core.integrals.MarchaudIntegral method) (hpfracc.core.integrals.MillerRossIntegral method) (hpfracc.core.integrals.RiemannLiouvilleIntegral method) (hpfracc.core.integrals.WeylIntegral method) (hpfracc.RiemannLiouvilleIntegral method) _compute_serial() (hpfracc.algorithms.advanced_methods.WeylDerivative method) (hpfracc.WeylDerivative method) _compute_single_term() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method) _compute_spectral() (hpfracc.algorithms.advanced_methods.ReizFellerDerivative method) (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedReizFellerDerivative method) (hpfracc.ReizFellerDerivative method) _compute_spectral_transform() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method) _compute_standard() (hpfracc.algorithms.advanced_methods.MarchaudDerivative method) (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedMarchaudDerivative method) (hpfracc.MarchaudDerivative method) _compute_standard_fft() (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedWeylDerivative method) _compute_terms_parallel() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method) _compute_terms_serial() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method) _compute_transform_matrix() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.FractionalFourierTransform method) _compute_weyl_discrete_legacy() (hpfracc.algorithms.integral_methods.WeylIntegral method) _compute_weyl_kernel() (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedWeylDerivative method) _compute_z_transform() (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedMarchaudDerivative method) _contour_integration() (hpfracc.algorithms.fractional_operator_methods.FractionalZTransform method) (hpfracc.FractionalZTransform method) _detect_available_backends() (hpfracc.ml.backends.BackendManager method) (hpfracc.ml.layers.BackendManager method) _determine_optimal_method() (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedWeylDerivative method) _direct_method() (hpfracc.algorithms.fractional_operator_methods.FractionalZTransform method) (hpfracc.FractionalZTransform method) _discrete_method() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.FractionalFourierTransform method) _dispatch() (hpfracc.algorithms.derivatives.UnifiedFractionalOperator method) _factorial() (in module hpfracc.algorithms.fractional_operator_methods) _fallback_compute() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method) _fast_approximation() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.FractionalFourierTransform method) _fft_based_method() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.FractionalFourierTransform method) _fft_method() (hpfracc.algorithms.fractional_operator_methods.FractionalMellinTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalZTransform method) (hpfracc.FractionalMellinTransform method) (hpfracc.FractionalZTransform method) _finite_difference_method() (hpfracc.algorithms.fractional_operator_methods.FractionalLaplacian method) (hpfracc.FractionalLaplacian method) _fractional_hermite() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.FractionalFourierTransform method) _gpu_sample_indices() (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method) _grunwald_coefficients() (hpfracc.algorithms.fractional_operator_methods.FractionalLaplacian method) (hpfracc.FractionalLaplacian method) _handle_backend_failure() (in module hpfracc.algorithms.derivatives) _handle_integration_failure() (in module hpfracc.core.integrals) _hermite_decomposition() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.FractionalFourierTransform method) _hermite_function() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.FractionalFourierTransform method) _initialize_backend_configs() (hpfracc.ml.backends.BackendManager method) _initialize_layer() (hpfracc.ml.gnn_layers.FractionalGraphConv method) _initialize_weights() (hpfracc.ml.core.FractionalAttention method) (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.layers.FractionalConv1D method) (hpfracc.ml.layers.FractionalConv2D method) (hpfracc.ml.layers.FractionalLinear method) _integral_method() (hpfracc.algorithms.fractional_operator_methods.FractionalLaplacian method) (hpfracc.FractionalLaplacian method) _inverse_fft() (hpfracc.algorithms.fractional_operator_methods.FractionalMellinTransform method) (hpfracc.FractionalMellinTransform method) _inverse_numerical() (hpfracc.algorithms.fractional_operator_methods.FractionalMellinTransform method) (hpfracc.FractionalMellinTransform method) _LegacyGPUShim (class in hpfracc.algorithms.optimized_methods) _log_variance_summary() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method) _numerical_method() (hpfracc.algorithms.fractional_operator_methods.FractionalMellinTransform method) (hpfracc.FractionalMellinTransform method) _numpy_trapezoid() (in module hpfracc.algorithms.fractional_operator_methods) _process_chunk() (hpfracc.algorithms.advanced_methods.WeylDerivative method) (hpfracc.WeylDerivative method) _process_chunks() (hpfracc.ml.gpu_optimization.ChunkedFFT method) _process_marchaud_chunk() (hpfracc.algorithms.advanced_methods.MarchaudDerivative method) (hpfracc.MarchaudDerivative method) _register_hooks() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method) _residue_method() (hpfracc.algorithms.fractional_operator_methods.FractionalZTransform method) (hpfracc.FractionalZTransform method) _select_optimal_backend() (hpfracc.ml.backends.BackendManager method) _select_optimal_method() (hpfracc.algorithms.integral_methods.RiemannLiouvilleIntegral method) _setup_layer() (hpfracc.ml.layers.FractionalLayerBase method) _spectral_method() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalLaplacian method) (hpfracc.FractionalFourierTransform method) (hpfracc.FractionalLaplacian method) _validate() (hpfracc.FractionalOrder method) _validate_chain() (hpfracc.core.derivatives.FractionalDerivativeChain method) _validate_parameters() (hpfracc.core.derivatives.BaseFractionalDerivative method) (hpfracc.core.integrals.FractionalIntegral method)

A

abs() (hpfracc.ml.tensor_ops.TensorOps method) activation (hpfracc.ml.layers.LayerConfig attribute) adam_step() (hpfracc.ml.tensor_ops.TensorOps method) AdaptiveSamplingManager (class in hpfracc.ml.variance_aware_training) add() (hpfracc.ml.tensor_ops.TensorOps method) AdomianDecomposition (class in hpfracc.algorithms.advanced_methods) AdomianDecompositionMethod (class in hpfracc.core.fractional_implementations) AdvancedFFTMethods (class in hpfracc.algorithms.optimized_methods) alpha (hpfracc.ml.spectral_autograd.BoundedAlphaParameter property) (hpfracc.ml.spectral_autograd.SpectralFractionalLayer property) AMPFractionalEngine (class in hpfracc.ml.gpu_optimization)

analytical_fractional_integral() (in module hpfracc.core.integrals) apply() (hpfracc.ml.spectral_autograd.SpectralFractionalDerivative static method) apply_activation() (hpfracc.ml.layers.FractionalLayerBase method) apply_dropout() (hpfracc.ml.layers.FractionalLayerBase method) apply_fractional_derivative() (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method) (hpfracc.ml.layers.FractionalLayerBase method) (hpfracc.ml.layers.FractionalOps method) arange() (hpfracc.ml.tensor_ops.TensorOps method) AtanganaBaleanuDerivative (class in hpfracc) (class in hpfracc.core.fractional_implementations) AUTO (hpfracc.ml.backends.BackendType attribute) avg_pool() (hpfracc.ml.tensor_ops.TensorOps method)

B

backend (hpfracc.ml.core.MLConfig attribute) (hpfracc.ml.layers.LayerConfig attribute) BackendManager (class in hpfracc.ml.backends) (class in hpfracc.ml.layers) BackendType (class in hpfracc.ml.backends) backward() (hpfracc.ml.gpu_optimization.AMPFractionalEngine method) (hpfracc.ml.spectral_autograd.SpectralFractionalFunction static method) (hpfracc.ml.tensor_ops.TensorOps method) balance_load() (hpfracc.algorithms.optimized_methods.ParallelLoadBalancer method) BaseFractionalDerivative (class in hpfracc.core.derivatives)

BaseFractionalGNN (class in hpfracc.ml.gnn_models) BaseFractionalGNNLayer (class in hpfracc.ml.gnn_layers) batch_norm() (hpfracc.ml.tensor_ops.TensorOps method) batch_size (hpfracc.ml.core.MLConfig attribute) benchmark_backends() (in module hpfracc.ml.spectral_autograd) benchmark_gpu_optimization() (in module hpfracc.ml.gpu_optimization) benchmark_gpu_vs_cpu() (in module hpfracc.algorithms.optimized_methods) benchmark_parallel_vs_serial() (in module hpfracc.algorithms.optimized_methods) block_processing_kernel() (in module hpfracc.algorithms.optimized_methods) BoundedAlphaParameter (class in hpfracc.ml.spectral_autograd)

C

Caputo (class in hpfracc.algorithms.derivatives) (in module hpfracc) caputo() (in module hpfracc.core.derivatives) caputo_integral() (in module hpfracc.algorithms.integral_methods) CaputoDerivative (class in hpfracc) (class in hpfracc.core.fractional_implementations) CaputoFabrizioDerivative (class in hpfracc) (class in hpfracc.core.fractional_implementations) CaputoIntegral (class in hpfracc) (class in hpfracc.algorithms.integral_methods) (class in hpfracc.core.integrals) cat() (hpfracc.ml.tensor_ops.TensorOps method) check_linearity() (hpfracc.core.derivatives.FractionalDerivativeProperties static method) check_semigroup_property() (hpfracc.core.derivatives.FractionalDerivativeProperties static method) ChunkedFFT (class in hpfracc.ml.gpu_optimization) clear_cache() (hpfracc.ml.tensor_ops.TensorOps method) clear_history() (hpfracc.ml.gpu_optimization.GPUProfiler method) clip() (hpfracc.ml.tensor_ops.TensorOps method) coefficient_of_variation (hpfracc.ml.variance_aware_training.VarianceMetrics attribute) compile_function() (hpfracc.ml.backends.BackendManager method) compute() (hpfracc.algorithms.advanced_methods.HadamardDerivative method) (hpfracc.algorithms.advanced_methods.MarchaudDerivative method) (hpfracc.algorithms.advanced_methods.ReizFellerDerivative method) (hpfracc.algorithms.advanced_methods.WeylDerivative method) (hpfracc.algorithms.derivatives.Caputo method) (hpfracc.algorithms.derivatives.GrunwaldLetnikov method) (hpfracc.algorithms.derivatives.RiemannLiouville method) (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalLaplacian method) (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedMarchaudDerivative method) (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedReizFellerDerivative method) (hpfracc.algorithms.fractional_operator_methods.SpecialOptimizedWeylDerivative method) (hpfracc.algorithms.integral_methods.CaputoIntegral method) (hpfracc.algorithms.integral_methods.RiemannLiouvilleIntegral method) (hpfracc.algorithms.integral_methods.WeylIntegral method) (hpfracc.algorithms.optimized_methods.GPUOptimizedCaputo method) (hpfracc.algorithms.optimized_methods.OptimizedFractionalMethods method) (hpfracc.AtanganaBaleanuDerivative method) (hpfracc.CaputoDerivative method) (hpfracc.CaputoFabrizioDerivative method) (hpfracc.CaputoIntegral method) (hpfracc.core.derivatives.BaseFractionalDerivative method) (hpfracc.core.derivatives.FractionalDerivativeChain method) (hpfracc.core.fractional_implementations.AtanganaBaleanuDerivative method) (hpfracc.core.fractional_implementations.CaputoDerivative method) (hpfracc.core.fractional_implementations.CaputoFabrizioDerivative method) (hpfracc.core.fractional_implementations.FractionalFourierTransform method) (hpfracc.core.fractional_implementations.FractionalLaplacian method) (hpfracc.core.fractional_implementations.GrunwaldLetnikovDerivative method) (hpfracc.core.fractional_implementations.HadamardDerivative method) (hpfracc.core.fractional_implementations.MarchaudDerivative method) (hpfracc.core.fractional_implementations.MillerRossDerivative method) (hpfracc.core.fractional_implementations.ReizFellerDerivative method) (hpfracc.core.fractional_implementations.RiemannLiouvilleDerivative method) (hpfracc.core.fractional_implementations.RieszFisherOperator method) (hpfracc.core.fractional_implementations.WeylDerivative method) (hpfracc.core.integrals.CaputoIntegral method) (hpfracc.core.integrals.FractionalIntegral method) (hpfracc.core.integrals.RiemannLiouvilleIntegral method) (hpfracc.core.integrals.WeylIntegral method) (hpfracc.FractionalFourierTransform method) (hpfracc.FractionalLaplacian method) (hpfracc.GrunwaldLetnikovDerivative method) (hpfracc.HadamardDerivative method) (hpfracc.MarchaudDerivative method) (hpfracc.ReizFellerDerivative method) (hpfracc.RiemannLiouvilleDerivative method) (hpfracc.RiemannLiouvilleIntegral method) (hpfracc.WeylDerivative method) compute_adomian_polynomials() (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method) compute_baseline() (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method) compute_derivative() (hpfracc.algorithms.fractional_operator_methods.UnifiedSpecialMethods method) compute_loss() (hpfracc.ml.core.FractionalCrossEntropyLoss method) (hpfracc.ml.core.FractionalLossFunction method) (hpfracc.ml.core.FractionalMSELoss method) (hpfracc.ml.losses.FractionalBCELoss method) (hpfracc.ml.losses.FractionalCombinedLoss method) (hpfracc.ml.losses.FractionalCosineEmbeddingLoss method) (hpfracc.ml.losses.FractionalCrossEntropyLoss method) (hpfracc.ml.losses.FractionalCTCLoss method) (hpfracc.ml.losses.FractionalCustomLoss method) (hpfracc.ml.losses.FractionalHuberLoss method) (hpfracc.ml.losses.FractionalKLDivergenceLoss method) (hpfracc.ml.losses.FractionalKLDivLoss method) (hpfracc.ml.losses.FractionalLossFunction method) (hpfracc.ml.losses.FractionalMarginRankingLoss method) (hpfracc.ml.losses.FractionalMomentMatchingLoss method) (hpfracc.ml.losses.FractionalMSELoss method) (hpfracc.ml.losses.FractionalMultiMarginLoss method) (hpfracc.ml.losses.FractionalNLLLoss method) (hpfracc.ml.losses.FractionalPathwiseLoss method) (hpfracc.ml.losses.FractionalPoissonNLLLoss method) (hpfracc.ml.losses.FractionalSDEMSELoss method) (hpfracc.ml.losses.FractionalSmoothL1Loss method) (hpfracc.ml.losses.FractionalTripletMarginLoss method)

compute_numerical() (hpfracc.algorithms.derivatives.UnifiedFractionalOperator method) (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalLaplacian method) (hpfracc.AtanganaBaleanuDerivative method) (hpfracc.CaputoDerivative method) (hpfracc.CaputoFabrizioDerivative method) (hpfracc.core.derivatives.BaseFractionalDerivative method) (hpfracc.core.derivatives.FractionalDerivativeOperator method) (hpfracc.core.fractional_implementations.AtanganaBaleanuDerivative method) (hpfracc.core.fractional_implementations.CaputoDerivative method) (hpfracc.core.fractional_implementations.CaputoFabrizioDerivative method) (hpfracc.core.fractional_implementations.FractionalFourierTransform method) (hpfracc.core.fractional_implementations.FractionalLaplacian method) (hpfracc.core.fractional_implementations.GrunwaldLetnikovDerivative method) (hpfracc.core.fractional_implementations.HadamardDerivative method) (hpfracc.core.fractional_implementations.MarchaudDerivative method) (hpfracc.core.fractional_implementations.MillerRossDerivative method) (hpfracc.core.fractional_implementations.ReizFellerDerivative method) (hpfracc.core.fractional_implementations.RiemannLiouvilleDerivative method) (hpfracc.core.fractional_implementations.RieszFisherOperator method) (hpfracc.core.fractional_implementations.WeylDerivative method) (hpfracc.FractionalFourierTransform method) (hpfracc.FractionalLaplacian method) (hpfracc.GrunwaldLetnikovDerivative method) (hpfracc.RiemannLiouvilleDerivative method) compute_weights() (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method) (hpfracc.ml.stochastic_memory_sampling.ImportanceSampler method) (hpfracc.ml.stochastic_memory_sampling.StochasticMemorySampler method) (hpfracc.ml.stochastic_memory_sampling.StratifiedSampler method) concatenate() (hpfracc.ml.tensor_ops.TensorOps method) ControlVariateSampler (class in hpfracc.ml.stochastic_memory_sampling) convolve() (hpfracc.ml.tensor_ops.TensorOps method) cos() (hpfracc.ml.tensor_ops.TensorOps method) create() (hpfracc.core.derivatives.FractionalDerivativeFactory method) (hpfracc.core.integrals.FractionalIntegralFactory method) create_beta_alpha_layer() (in module hpfracc.ml.probabilistic_fractional_orders) create_derivative_operator() (in module hpfracc.core.derivatives) create_fractional_derivative() (in module hpfracc.core.derivatives) create_fractional_integral() (in module hpfracc.core.fractional_implementations) (in module hpfracc.core.integrals) create_fractional_integral_factory() (in module hpfracc.core.integrals) create_fractional_layer() (in module hpfracc.ml.spectral_autograd) create_gpu_optimized_components() (in module hpfracc.ml.gpu_optimization) create_model() (hpfracc.ml.gnn_models.FractionalGNNFactory static method) create_normal_alpha_layer() (in module hpfracc.ml.probabilistic_fractional_orders) create_optimized_adam() (in module hpfracc.ml.optimized_optimizers) create_optimized_sgd() (in module hpfracc.ml.optimized_optimizers) create_probabilistic_fractional_layer() (in module hpfracc.ml.probabilistic_fractional_orders) create_riesz_fisher_operator() (in module hpfracc.core.fractional_implementations) create_stochastic_fractional_layer() (in module hpfracc.ml.stochastic_memory_sampling) create_tensor() (hpfracc.ml.backends.BackendManager method) (hpfracc.ml.tensor_ops.TensorOps method) (in module hpfracc.ml.tensor_ops) create_uniform_alpha_layer() (in module hpfracc.ml.probabilistic_fractional_orders) create_variance_aware_trainer() (in module hpfracc.ml.variance_aware_training) cross_entropy_loss() (hpfracc.ml.tensor_ops.TensorOps method) current_metrics (hpfracc.ml.gpu_optimization.GPUProfiler attribute) (hpfracc.ml.variance_aware_training.VarianceMonitor property)

D

decompose_function() (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method) device (hpfracc.ml.core.MLConfig attribute) (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute) (hpfracc.ml.layers.LayerConfig attribute) device() (hpfracc.ml.tensor_ops.TensorOps method)

divide() (hpfracc.ml.tensor_ops.TensorOps method) dropout (hpfracc.ml.layers.LayerConfig attribute) dropout() (hpfracc.ml.tensor_ops.TensorOps method) dtype (hpfracc.ml.core.MLConfig attribute) (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute)

E

early_stopping_patience (hpfracc.ml.core.MLConfig attribute) enable_benchmarking (hpfracc.ml.layers.LayerConfig attribute) enable_caching (hpfracc.ml.layers.LayerConfig attribute) enable_deterministic_mode() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method) enable_monitoring() (hpfracc.algorithms.optimized_methods.GPUOptimizedRiemannLiouville method) enable_profiling() (hpfracc.ml.tensor_ops.TensorOps method) end_timer() (hpfracc.ml.gpu_optimization.GPUProfiler method) equal() (hpfracc.ml.tensor_ops.TensorOps method) estimate_derivative() (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method) (hpfracc.ml.stochastic_memory_sampling.ImportanceSampler method) (hpfracc.ml.stochastic_memory_sampling.StochasticMemorySampler method) (hpfracc.ml.stochastic_memory_sampling.StratifiedSampler method)

eval() (hpfracc.ml.core.FractionalAttention method) (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_layers.FractionalGraphConv method) execution_time (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute) exp() (hpfracc.ml.tensor_ops.TensorOps method) expand() (hpfracc.ml.tensor_ops.TensorOps method) extra_repr() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method) (hpfracc.ml.spectral_autograd.BoundedAlphaParameter method) (hpfracc.ml.stochastic_memory_sampling.StochasticFractionalLayer method) eye() (hpfracc.ml.tensor_ops.TensorOps method)

F

fft() (hpfracc.ml.tensor_ops.TensorOps method) fft_chunked() (hpfracc.ml.gpu_optimization.ChunkedFFT method) forward() (hpfracc.ml.core.FractionalAttention method) (hpfracc.ml.core.FractionalLossFunction method) (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_layers.BaseFractionalGNNLayer method) (hpfracc.ml.gnn_layers.FractionalGraphAttention method) (hpfracc.ml.gnn_layers.FractionalGraphConv method) (hpfracc.ml.gnn_layers.FractionalGraphPooling method) (hpfracc.ml.gnn_models.BaseFractionalGNN method) (hpfracc.ml.gnn_models.FractionalGAT method) (hpfracc.ml.gnn_models.FractionalGCN method) (hpfracc.ml.gnn_models.FractionalGraphSAGE method) (hpfracc.ml.gnn_models.FractionalGraphUNet method) (hpfracc.ml.gpu_optimization.AMPFractionalEngine method) (hpfracc.ml.gpu_optimization.ChunkedFFT method) (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method) (hpfracc.ml.layers.FractionalBatchNorm1d method) (hpfracc.ml.layers.FractionalConv1D method) (hpfracc.ml.layers.FractionalConv2D method) (hpfracc.ml.layers.FractionalDropout method) (hpfracc.ml.layers.FractionalLayerBase method) (hpfracc.ml.layers.FractionalLayerNorm method) (hpfracc.ml.layers.FractionalLinear method) (hpfracc.ml.layers.FractionalLSTM method) (hpfracc.ml.layers.FractionalMaxUnpool1d method) (hpfracc.ml.layers.FractionalMaxUnpool2d method) (hpfracc.ml.layers.FractionalMaxUnpool3d method) (hpfracc.ml.layers.FractionalPooling method) (hpfracc.ml.layers.FractionalSelfAttention method) (hpfracc.ml.layers.FractionalTransformer method) (hpfracc.ml.losses.FractionalLossFunction method) (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method) (hpfracc.ml.spectral_autograd.BoundedAlphaParameter method) (hpfracc.ml.spectral_autograd.SpectralFractionalFunction static method) (hpfracc.ml.spectral_autograd.SpectralFractionalLayer method) (hpfracc.ml.spectral_autograd.SpectralFractionalNetwork method) (hpfracc.ml.stochastic_memory_sampling.StochasticFractionalLayer method) forward_with_state() (hpfracc.ml.layers.FractionalLSTM method) fractional_attention() (hpfracc.ml.core.FractionalAttention method) fractional_derivative() (in module hpfracc.ml.spectral_autograd) fractional_forward() (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.losses.FractionalLossFunction method) fractional_fourier_transform() (in module hpfracc.algorithms.fractional_operator_methods) fractional_integral_properties() (in module hpfracc.core.integrals) fractional_laplacian() (in module hpfracc.algorithms.fractional_operator_methods) fractional_loss() (hpfracc.ml.core.FractionalLossFunction method) fractional_mellin_transform() (in module hpfracc.algorithms.fractional_operator_methods) fractional_order (hpfracc.ml.core.MLConfig attribute) (hpfracc.ml.layers.LayerConfig attribute) fractional_part (hpfracc.FractionalOrder property) fractional_z_transform() (in module hpfracc.algorithms.fractional_operator_methods) FractionalAttention (class in hpfracc.ml.core) FractionalAutoML (class in hpfracc.ml.core) FractionalBatchNorm1d (class in hpfracc.ml.layers) FractionalBCELoss (class in hpfracc.ml.losses) FractionalCombinedLoss (class in hpfracc.ml.losses) FractionalConv1D (class in hpfracc.ml.layers) FractionalConv2D (class in hpfracc.ml.layers) FractionalCosineEmbeddingLoss (class in hpfracc.ml.losses)

FractionalCrossEntropyLoss (class in hpfracc.ml.core) (class in hpfracc.ml.losses) FractionalCTCLoss (class in hpfracc.ml.losses) FractionalCustomLoss (class in hpfracc.ml.losses) FractionalDerivativeChain (class in hpfracc.core.derivatives) FractionalDerivativeFactory (class in hpfracc.core.derivatives) FractionalDerivativeOperator (class in hpfracc.core.derivatives) FractionalDerivativeProperties (class in hpfracc.core.derivatives) FractionalDropout (class in hpfracc.ml.layers) FractionalFourierTransform (class in hpfracc) (class in hpfracc.algorithms.fractional_operator_methods) (class in hpfracc.core.fractional_implementations) FractionalGAT (class in hpfracc.ml.gnn_models) FractionalGCN (class in hpfracc.ml.gnn_models) FractionalGNNFactory (class in hpfracc.ml.gnn_models) FractionalGraphAttention (class in hpfracc.ml.gnn_layers) FractionalGraphConv (class in hpfracc.ml.gnn_layers) FractionalGraphPooling (class in hpfracc.ml.gnn_layers) FractionalGraphSAGE (class in hpfracc.ml.gnn_models) FractionalGraphUNet (class in hpfracc.ml.gnn_models) FractionalHuberLoss (class in hpfracc.ml.losses) FractionalIntegral (class in hpfracc.core.integrals) FractionalIntegralFactory (class in hpfracc.core.integrals) FractionalKLDivergenceLoss (class in hpfracc.ml.losses) FractionalKLDivLoss (class in hpfracc.ml.losses) FractionalLaplacian (class in hpfracc) (class in hpfracc.algorithms.fractional_operator_methods) (class in hpfracc.core.fractional_implementations) FractionalLayerBase (class in hpfracc.ml.layers) FractionalLayerNorm (class in hpfracc.ml.layers) FractionalLinear (class in hpfracc.ml.layers) FractionalLossFunction (class in hpfracc.ml.core) (class in hpfracc.ml.losses) FractionalLSTM (class in hpfracc.ml.layers) FractionalMarginRankingLoss (class in hpfracc.ml.losses) FractionalMaxUnpool1d (class in hpfracc.ml.layers) FractionalMaxUnpool2d (class in hpfracc.ml.layers) FractionalMaxUnpool3d (class in hpfracc.ml.layers) FractionalMellinTransform (class in hpfracc) (class in hpfracc.algorithms.fractional_operator_methods) FractionalMomentMatchingLoss (class in hpfracc.ml.losses) FractionalMSELoss (class in hpfracc.ml.core) (class in hpfracc.ml.losses) FractionalMultiMarginLoss (class in hpfracc.ml.losses) FractionalNeuralNetwork (class in hpfracc.ml.core) FractionalNLLLoss (class in hpfracc.ml.losses) FractionalOps (class in hpfracc.ml.layers) FractionalOptimizer (class in hpfracc.ml.optimized_optimizers) FractionalOrder (class in hpfracc) FractionalPathwiseLoss (class in hpfracc.ml.losses) FractionalPoissonNLLLoss (class in hpfracc.ml.losses) FractionalPooling (class in hpfracc.ml.layers) FractionalSDEMSELoss (class in hpfracc.ml.losses) FractionalSelfAttention (class in hpfracc.ml.layers) FractionalSmoothL1Loss (class in hpfracc.ml.losses) FractionalTransformer (class in hpfracc.ml.layers) FractionalTripletMarginLoss (class in hpfracc.ml.losses) FractionalZTransform (class in hpfracc) (class in hpfracc.algorithms.fractional_operator_methods) from_numpy() (hpfracc.ml.tensor_ops.TensorOps method)

G

gather() (hpfracc.ml.tensor_ops.TensorOps method) get_active_backend() (in module hpfracc.ml.backends) get_alpha() (hpfracc.ml.spectral_autograd.SpectralFractionalLayer method) get_alpha_statistics() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method) get_analytical_solutions() (hpfracc.core.derivatives.FractionalDerivativeProperties static method) get_available_implementations() (hpfracc.core.derivatives.FractionalDerivativeFactory method) get_available_methods() (hpfracc.core.integrals.FractionalIntegralFactory method) get_available_models() (hpfracc.ml.gnn_models.FractionalGNNFactory static method) get_backend_config() (hpfracc.ml.backends.BackendManager method) get_backend_info() (hpfracc.ml.gnn_models.BaseFractionalGNN method) (hpfracc.ml.tensor_ops.TensorOps method) get_backend_manager() (in module hpfracc.ml.backends) get_best_model() (hpfracc.ml.core.FractionalAutoML method) get_chain_info() (hpfracc.core.derivatives.FractionalDerivativeChain method) get_chunk_sizes() (hpfracc.algorithms.optimized_methods.ParallelLoadBalancer method) get_current_k() (hpfracc.ml.variance_aware_training.AdaptiveSamplingManager method) get_definition_info() (hpfracc.core.derivatives.BaseFractionalDerivative method) get_fft_backend() (in module hpfracc.ml.spectral_autograd) get_history() (hpfracc.ml.variance_aware_training.VarianceMonitor method) get_info() (hpfracc.core.derivatives.FractionalDerivativeOperator method) get_memory_usage() (hpfracc.ml.tensor_ops.TensorOps method) get_metrics() (hpfracc.ml.variance_aware_training.VarianceMonitor method) get_model_info() (hpfracc.ml.gnn_models.FractionalGNNFactory static method) get_next_seed() (hpfracc.ml.variance_aware_training.StochasticSeedManager method) get_optimal_workers() (hpfracc.algorithms.optimized_methods.ParallelConfig method) get_performance_summary() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method) (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method)

get_profile_results() (hpfracc.ml.tensor_ops.TensorOps method) get_scaler_state() (hpfracc.ml.gpu_optimization.AMPFractionalEngine method) get_summary() (hpfracc.ml.gpu_optimization.GPUProfiler method) (hpfracc.ml.variance_aware_training.VarianceMonitor method) get_tensor_lib() (hpfracc.ml.backends.BackendManager method) get_tensor_ops() (in module hpfracc.ml.tensor_ops) get_total_order() (hpfracc.core.derivatives.FractionalDerivativeChain method) get_variance_summary() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method) gpu_optimization_context() (in module hpfracc.ml.gpu_optimization) gpu_optimized_caputo() (in module hpfracc.algorithms.optimized_methods) gpu_optimized_grunwald_letnikov() (in module hpfracc.algorithms.optimized_methods) gpu_optimized_riemann_liouville() (in module hpfracc.algorithms.optimized_methods) GPUConfig (class in hpfracc.algorithms.optimized_methods) GPUOptimizedCaputo (class in hpfracc.algorithms.optimized_methods) GPUOptimizedGrunwaldLetnikov (class in hpfracc.algorithms.optimized_methods) GPUOptimizedMethods (class in hpfracc.algorithms.optimized_methods) GPUOptimizedRiemannLiouville (class in hpfracc.algorithms.optimized_methods) GPUOptimizedSpectralEngine (class in hpfracc.ml.gpu_optimization) GPUOptimizedStochasticSampler (class in hpfracc.ml.gpu_optimization) GPUProfiler (class in hpfracc.ml.gpu_optimization) grad() (hpfracc.ml.tensor_ops.TensorOps method) greater() (hpfracc.ml.tensor_ops.TensorOps method) grunwald_letnikov() (in module hpfracc.core.derivatives) GrunwaldLetnikov (class in hpfracc.algorithms.derivatives) (in module hpfracc) GrunwaldLetnikovDerivative (class in hpfracc) (class in hpfracc.core.fractional_implementations) guide() (in module hpfracc.ml.probabilistic_fractional_orders)

H

hadamard_derivative() (in module hpfracc.algorithms.advanced_methods) HadamardDerivative (class in hpfracc) (class in hpfracc.algorithms.advanced_methods) (class in hpfracc.core.fractional_implementations) HadamardIntegral (class in hpfracc.core.integrals) hpfracc module hpfracc.algorithms.advanced_methods module hpfracc.algorithms.derivatives module hpfracc.algorithms.fractional_operator_methods module hpfracc.algorithms.integral_methods module hpfracc.algorithms.optimized_methods module hpfracc.core.definitions.DEFAULT_FRACTIONAL_ORDER (in module hpfracc.ml.optimized_optimizers) hpfracc.core.derivatives module hpfracc.core.derivatives.SUPPORTED_METHODS (in module hpfracc.ml.optimized_optimizers) hpfracc.core.fractional_implementations module hpfracc.core.integrals module hpfracc.ml.backends module

hpfracc.ml.backends.DEFAULT_BACKEND (in module hpfracc.ml.optimized_optimizers) hpfracc.ml.backends.SUPPORTED_BACKENDS (in module hpfracc.ml.optimized_optimizers) hpfracc.ml.core module hpfracc.ml.gnn_layers module hpfracc.ml.gnn_models module hpfracc.ml.gnn_models.SUPPORTED_GNN_TYPES (in module hpfracc.ml.optimized_optimizers) hpfracc.ml.gpu_optimization module hpfracc.ml.layers module hpfracc.ml.losses module hpfracc.ml.optimized_optimizers module hpfracc.ml.probabilistic_fractional_orders module hpfracc.ml.spectral_autograd module hpfracc.ml.stochastic_memory_sampling module hpfracc.ml.tensor_ops module hpfracc.ml.tensor_ops.DEFAULT_DTYPE (in module hpfracc.ml.optimized_optimizers) hpfracc.ml.variance_aware_training module

I

ifft() (hpfracc.ml.tensor_ops.TensorOps method) ifft_chunked() (hpfracc.ml.gpu_optimization.ChunkedFFT method) ImportanceSampler (class in hpfracc.ml.stochastic_memory_sampling) index() (hpfracc.ml.tensor_ops.TensorOps method) init() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalOrder method) input_shape (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute) integer_part (hpfracc.FractionalOrder property)

inverse() (hpfracc.ml.gpu_optimization.ChunkedFFT method) (hpfracc.ml.tensor_ops.TensorOps method) inverse_transform() (hpfracc.algorithms.fractional_operator_methods.FractionalMellinTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalZTransform method) (hpfracc.FractionalMellinTransform method) (hpfracc.FractionalZTransform method) is_fractional (hpfracc.FractionalOrder property) is_integer (hpfracc.FractionalOrder property)

J

JAX (hpfracc.ml.backends.BackendType attribute)

L

L1L2Schemes (class in hpfracc.algorithms.optimized_methods) layer_norm() (hpfracc.ml.tensor_ops.TensorOps method) LayerConfig (class in hpfracc.ml.layers) learnable (hpfracc.ml.spectral_autograd.SpectralFractionalLayer property) learning_rate (hpfracc.ml.core.MLConfig attribute) less() (hpfracc.ml.tensor_ops.TensorOps method) linspace() (hpfracc.ml.tensor_ops.TensorOps method)

load_model() (hpfracc.ml.core.FractionalNeuralNetwork class method) load_state_dict() (hpfracc.ml.gnn_layers.FractionalGraphConv method) log() (hpfracc.ml.tensor_ops.TensorOps method) log_interval (hpfracc.ml.core.MLConfig attribute) log_prob() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalOrder method) logical_and() (hpfracc.ml.tensor_ops.TensorOps method) logical_not() (hpfracc.ml.tensor_ops.TensorOps method) logical_or() (hpfracc.ml.tensor_ops.TensorOps method)

M

marchaud_derivative() (in module hpfracc.algorithms.advanced_methods) MarchaudDerivative (class in hpfracc) (class in hpfracc.algorithms.advanced_methods) (class in hpfracc.core.fractional_implementations) MarchaudIntegral (class in hpfracc.core.integrals) matmul() (hpfracc.ml.tensor_ops.TensorOps method) max() (hpfracc.ml.tensor_ops.TensorOps method) max_epochs (hpfracc.ml.core.MLConfig attribute) max_pool() (hpfracc.ml.tensor_ops.TensorOps method) maximum() (hpfracc.ml.tensor_ops.TensorOps method) mean (hpfracc.ml.variance_aware_training.VarianceMetrics attribute) mean() (hpfracc.ml.tensor_ops.TensorOps method) memory_efficient_caputo() (in module hpfracc.algorithms.optimized_methods) memory_peak (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute) memory_used (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute) method (hpfracc.ml.layers.LayerConfig attribute) metrics_history (hpfracc.ml.gpu_optimization.GPUProfiler attribute) (hpfracc.ml.variance_aware_training.VarianceMonitor attribute) MillerRossDerivative (class in hpfracc.core.fractional_implementations) MillerRossIntegral (class in hpfracc.core.integrals) min() (hpfracc.ml.tensor_ops.TensorOps method) minimum() (hpfracc.ml.tensor_ops.TensorOps method) MLConfig (class in hpfracc.ml.core) model() (in module hpfracc.ml.probabilistic_fractional_orders) model_save_path (hpfracc.ml.core.MLConfig attribute)

module hpfracc hpfracc.algorithms.advanced_methods hpfracc.algorithms.derivatives hpfracc.algorithms.fractional_operator_methods hpfracc.algorithms.integral_methods hpfracc.algorithms.optimized_methods hpfracc.core.derivatives hpfracc.core.fractional_implementations hpfracc.core.integrals hpfracc.ml.backends hpfracc.ml.core hpfracc.ml.gnn_layers hpfracc.ml.gnn_models hpfracc.ml.gpu_optimization hpfracc.ml.layers hpfracc.ml.losses hpfracc.ml.optimized_optimizers hpfracc.ml.probabilistic_fractional_orders hpfracc.ml.spectral_autograd hpfracc.ml.stochastic_memory_sampling hpfracc.ml.tensor_ops hpfracc.ml.variance_aware_training mse_loss() (hpfracc.ml.tensor_ops.TensorOps method) MultiGPUManager (class in hpfracc.algorithms.optimized_methods) multiply() (hpfracc.ml.tensor_ops.TensorOps method)

N

named_parameters() (hpfracc.ml.gnn_layers.FractionalGraphConv method) no_grad() (hpfracc.ml.tensor_ops.TensorOps method) norm() (hpfracc.ml.tensor_ops.TensorOps method)

NUMBA (hpfracc.ml.backends.BackendType attribute) NumbaFractionalKernels (class in hpfracc.algorithms.optimized_methods) NumbaOptimizer (class in hpfracc.algorithms.optimized_methods) NumbaParallelManager (class in hpfracc.algorithms.optimized_methods)

O

on_batch_begin() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method) on_batch_end() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method) on_epoch_begin() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method) on_epoch_end() (hpfracc.ml.variance_aware_training.VarianceAwareCallback method) ones() (hpfracc.ml.tensor_ops.TensorOps method) ones_like() (hpfracc.ml.tensor_ops.TensorOps method) operation (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute) optimize_fractional_order() (hpfracc.ml.core.FractionalAutoML method) optimize_parallel_parameters() (in module hpfracc.algorithms.optimized_methods) optimized_caputo() (in module hpfracc.algorithms.optimized_methods) optimized_caputo_integral() (in module hpfracc.algorithms.integral_methods) optimized_grunwald_letnikov() (in module hpfracc.algorithms.optimized_methods) optimized_hadamard_derivative() (in module hpfracc.algorithms.advanced_methods) optimized_marchaud_derivative() (in module hpfracc.algorithms.advanced_methods) optimized_reiz_feller_derivative() (in module hpfracc.algorithms.advanced_methods) optimized_riemann_liouville() (in module hpfracc) (in module hpfracc.algorithms.optimized_methods) optimized_riemann_liouville_integral() (in module hpfracc.algorithms.integral_methods) optimized_weyl_derivative() (in module hpfracc.algorithms.advanced_methods) OptimizedAdomianDecomposition (in module hpfracc.algorithms.advanced_methods) OptimizedBaseOptimizer (in module hpfracc.ml.optimized_optimizers)

OptimizedCaputo (in module hpfracc) OptimizedFractionalAdam (class in hpfracc.ml.optimized_optimizers) OptimizedFractionalMethods (class in hpfracc.algorithms.optimized_methods) OptimizedFractionalRMSprop (class in hpfracc.ml.optimized_optimizers) OptimizedFractionalSGD (class in hpfracc.ml.optimized_optimizers) OptimizedGrunwaldLetnikov (in module hpfracc) OptimizedHadamardDerivative (in module hpfracc.algorithms.advanced_methods) OptimizedMarchaudDerivative (in module hpfracc.algorithms.advanced_methods) OptimizedReizFellerDerivative (in module hpfracc.algorithms.advanced_methods) OptimizedRiemannLiouville (in module hpfracc) OptimizedWeylDerivative (in module hpfracc.algorithms.advanced_methods) original_create_fractional_layer() (in module hpfracc.ml.spectral_autograd) original_get_fft_backend() (in module hpfracc.ml.spectral_autograd) original_get_fractional_kernel() (in module hpfracc.ml.spectral_autograd) original_safe_fft() (in module hpfracc.ml.spectral_autograd) original_safe_ifft() (in module hpfracc.ml.spectral_autograd) original_set_fft_backend() (in module hpfracc.ml.spectral_autograd) original_spectral_fractional_derivative() (in module hpfracc.ml.spectral_autograd) OriginalSpectral (in module hpfracc.ml.spectral_autograd) OriginalSpectralFractionalLayer (in module hpfracc.ml.spectral_autograd) OriginalSpectralFractionalNetwork (in module hpfracc.ml.spectral_autograd)

P

parallel_hadamard_derivative() (in module hpfracc.algorithms.advanced_methods) parallel_marchaud_derivative() (in module hpfracc.algorithms.advanced_methods) parallel_reiz_feller_derivative() (in module hpfracc.algorithms.advanced_methods) parallel_weyl_derivative() (in module hpfracc.algorithms.advanced_methods) ParallelAdomianDecomposition (class in hpfracc.algorithms.advanced_methods) ParallelConfig (class in hpfracc.algorithms.optimized_methods) ParallelHadamardDerivative (class in hpfracc.algorithms.advanced_methods) ParallelLoadBalancer (class in hpfracc.algorithms.optimized_methods) ParallelMarchaudDerivative (class in hpfracc.algorithms.advanced_methods) ParallelOptimizedCaputo (class in hpfracc.algorithms.optimized_methods) ParallelOptimizedGrunwaldLetnikov (class in hpfracc.algorithms.optimized_methods)

ParallelOptimizedRiemannLiouville (class in hpfracc.algorithms.optimized_methods) ParallelReizFellerDerivative (class in hpfracc.algorithms.advanced_methods) ParallelWeylDerivative (class in hpfracc.algorithms.advanced_methods) parameters() (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_layers.FractionalGraphConv method) (hpfracc.ml.gnn_models.BaseFractionalGNN method) performance_mode (hpfracc.ml.layers.LayerConfig attribute) PerformanceMetrics (class in hpfracc.ml.gpu_optimization) power() (hpfracc.ml.tensor_ops.TensorOps method) ProbabilisticFractionalLayer (class in hpfracc.ml.probabilistic_fractional_orders) ProbabilisticFractionalOrder (class in hpfracc.ml.probabilistic_fractional_orders)

R

random_normal() (hpfracc.ml.tensor_ops.TensorOps method) random_uniform() (hpfracc.ml.tensor_ops.TensorOps method) register_fractional_implementations() (in module hpfracc.core.fractional_implementations) register_implementation() (hpfracc.core.derivatives.FractionalDerivativeFactory method) (hpfracc.core.integrals.FractionalIntegralFactory method) reiz_feller_derivative() (in module hpfracc.algorithms.advanced_methods) ReizFellerDerivative (class in hpfracc) (class in hpfracc.algorithms.advanced_methods) (class in hpfracc.core.fractional_implementations) relu() (hpfracc.ml.tensor_ops.TensorOps method) repeat() (hpfracc.ml.tensor_ops.TensorOps method) reset_to_base() (hpfracc.ml.variance_aware_training.StochasticSeedManager method)

reshape() (hpfracc.ml.tensor_ops.TensorOps method) riemann_liouville() (in module hpfracc.core.derivatives) riemann_liouville_integral() (in module hpfracc.algorithms.integral_methods) RiemannLiouville (class in hpfracc.algorithms.derivatives) (in module hpfracc) RiemannLiouvilleDerivative (class in hpfracc) (class in hpfracc.core.fractional_implementations) RiemannLiouvilleIntegral (class in hpfracc) (class in hpfracc.algorithms.integral_methods) (class in hpfracc.core.integrals) RieszFisherOperator (class in hpfracc.core.fractional_implementations) robust_fft() (in module hpfracc.ml.spectral_autograd) robust_ifft() (in module hpfracc.ml.spectral_autograd)

S

safe_fft() (in module hpfracc.ml.spectral_autograd) safe_ifft() (in module hpfracc.ml.spectral_autograd) sample() (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method) (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalOrder method) sample_alpha() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method) sample_count (hpfracc.ml.variance_aware_training.VarianceMetrics attribute) sample_indices() (hpfracc.ml.gpu_optimization.GPUOptimizedStochasticSampler method) (hpfracc.ml.stochastic_memory_sampling.ControlVariateSampler method) (hpfracc.ml.stochastic_memory_sampling.ImportanceSampler method) (hpfracc.ml.stochastic_memory_sampling.StochasticMemorySampler method) (hpfracc.ml.stochastic_memory_sampling.StratifiedSampler method) save_model() (hpfracc.ml.core.FractionalNeuralNetwork method) select_backend_for_data() (hpfracc.algorithms.optimized_methods.GPUConfig method) select_optimal_backend() (hpfracc.ml.layers.BackendManager method) set_backend_manager() (in module hpfracc.ml.backends) set_deterministic_mode() (hpfracc.ml.variance_aware_training.StochasticSeedManager method) set_fft_backend() (in module hpfracc.ml.spectral_autograd) set_implementation() (hpfracc.core.derivatives.FractionalDerivativeOperator method) set_sampling_budget() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method) set_seed() (hpfracc.ml.variance_aware_training.StochasticSeedManager method) sgd_step() (hpfracc.ml.tensor_ops.TensorOps method) shape() (hpfracc.ml.tensor_ops.TensorOps method) should_adapt() (hpfracc.ml.variance_aware_training.VarianceMonitor method) sigmoid() (hpfracc.ml.tensor_ops.TensorOps method) sign() (hpfracc.ml.tensor_ops.TensorOps method) simpson_fractional_integral() (in module hpfracc.core.integrals) sin() (hpfracc.ml.tensor_ops.TensorOps method) slice() (hpfracc.ml.tensor_ops.TensorOps method) softmax() (hpfracc.ml.tensor_ops.TensorOps method) solve() (hpfracc.algorithms.advanced_methods.AdomianDecomposition method) (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method) solve_equation() (hpfracc.core.fractional_implementations.AdomianDecompositionMethod method) special_optimized_marchaud_derivative() (in module hpfracc.algorithms.fractional_operator_methods)

special_optimized_reiz_feller_derivative() (in module hpfracc.algorithms.fractional_operator_methods) special_optimized_weyl_derivative() (in module hpfracc.algorithms.fractional_operator_methods) SpecialMethodsConfig (class in hpfracc.algorithms.fractional_operator_methods) SpecialOptimizedMarchaudDerivative (class in hpfracc.algorithms.fractional_operator_methods) SpecialOptimizedReizFellerDerivative (class in hpfracc.algorithms.fractional_operator_methods) SpecialOptimizedWeylDerivative (class in hpfracc.algorithms.fractional_operator_methods) spectral_derivative() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method) spectral_fractional_derivative() (in module hpfracc.ml.spectral_autograd) spectral_integral() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method) spectral_transform() (hpfracc.ml.gpu_optimization.GPUOptimizedSpectralEngine method) SpectralFractionalDerivative (class in hpfracc.ml.spectral_autograd) SpectralFractionalFunction (class in hpfracc.ml.spectral_autograd) SpectralFractionalLayer (class in hpfracc.ml.spectral_autograd) SpectralFractionalNetwork (class in hpfracc.ml.spectral_autograd) sqrt() (hpfracc.ml.tensor_ops.TensorOps method) squeeze() (hpfracc.ml.tensor_ops.TensorOps method) stack() (hpfracc.ml.tensor_ops.TensorOps method) start_timer() (hpfracc.ml.gpu_optimization.GPUProfiler method) state_dict() (hpfracc.ml.gnn_layers.FractionalGraphConv method) std (hpfracc.ml.variance_aware_training.VarianceMetrics attribute) step() (hpfracc.ml.optimized_optimizers.OptimizedFractionalAdam method) (hpfracc.ml.optimized_optimizers.OptimizedFractionalRMSprop method) (hpfracc.ml.optimized_optimizers.OptimizedFractionalSGD method) stochastic_fractional_derivative() (in module hpfracc.ml.stochastic_memory_sampling) StochasticFractionalLayer (class in hpfracc.ml.stochastic_memory_sampling) StochasticMemorySampler (class in hpfracc.ml.stochastic_memory_sampling) StochasticSeedManager (class in hpfracc.ml.variance_aware_training) StratifiedSampler (class in hpfracc.ml.stochastic_memory_sampling) subtract() (hpfracc.ml.tensor_ops.TensorOps method) sum() (hpfracc.ml.tensor_ops.TensorOps method) switch_backend() (hpfracc.ml.backends.BackendManager method) (hpfracc.ml.tensor_ops.TensorOps method) (in module hpfracc.ml.backends) (in module hpfracc.ml.tensor_ops)

T

tanh() (hpfracc.ml.tensor_ops.TensorOps method) tensor() (hpfracc.ml.tensor_ops.TensorOps method) TensorOps (class in hpfracc.ml.tensor_ops) test_gpu_optimization() (in module hpfracc.ml.gpu_optimization) test_variance_aware_training() (in module hpfracc.ml.variance_aware_training) throughput (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute) tile() (hpfracc.ml.tensor_ops.TensorOps method) timestamp (hpfracc.ml.gpu_optimization.PerformanceMetrics attribute) (hpfracc.ml.variance_aware_training.VarianceMetrics attribute) to() (hpfracc.ml.probabilistic_fractional_orders.ProbabilisticFractionalLayer method) to_device() (hpfracc.ml.backends.BackendManager method) (hpfracc.ml.tensor_ops.TensorOps method) to_numpy() (hpfracc.ml.tensor_ops.TensorOps method)

TORCH (hpfracc.ml.backends.BackendType attribute) train() (hpfracc.ml.core.FractionalAttention method) (hpfracc.ml.core.FractionalNeuralNetwork method) (hpfracc.ml.gnn_layers.FractionalGraphConv method) (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method) train_epoch() (hpfracc.ml.variance_aware_training.VarianceAwareTrainer method) transform() (hpfracc.algorithms.fractional_operator_methods.FractionalFourierTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalMellinTransform method) (hpfracc.algorithms.fractional_operator_methods.FractionalZTransform method) (hpfracc.FractionalFourierTransform method) (hpfracc.FractionalMellinTransform method) (hpfracc.FractionalZTransform method) transpose() (hpfracc.ml.tensor_ops.TensorOps method) trapezoidal_fractional_integral() (in module hpfracc.core.integrals)

U

unified_special_derivative() (in module hpfracc.algorithms.fractional_operator_methods) UnifiedFractionalOperator (class in hpfracc.algorithms.derivatives) UnifiedSpecialMethods (class in hpfracc.algorithms.fractional_operator_methods) unsqueeze() (hpfracc.ml.tensor_ops.TensorOps method)

update() (hpfracc.ml.variance_aware_training.VarianceMonitor method) update_k() (hpfracc.ml.variance_aware_training.AdaptiveSamplingManager method) update_scaler() (hpfracc.ml.gpu_optimization.AMPFractionalEngine method) use_fractional (hpfracc.ml.layers.LayerConfig attribute) use_gpu (hpfracc.ml.core.MLConfig attribute)

V

validate_fractional_integral() (in module hpfracc.core.integrals) validation_split (hpfracc.ml.core.MLConfig attribute) value (hpfracc.FractionalOrder property) variance (hpfracc.ml.variance_aware_training.VarianceMetrics attribute)

VarianceAwareCallback (class in hpfracc.ml.variance_aware_training) VarianceAwareTrainer (class in hpfracc.ml.variance_aware_training) VarianceMetrics (class in hpfracc.ml.variance_aware_training) VarianceMonitor (class in hpfracc.ml.variance_aware_training)

W

weyl_derivative() (in module hpfracc.algorithms.advanced_methods) WeylDerivative (class in hpfracc) (class in hpfracc.algorithms.advanced_methods) (class in hpfracc.core.fractional_implementations)

WeylIntegral (class in hpfracc.algorithms.integral_methods) (class in hpfracc.core.integrals) where() (hpfracc.ml.tensor_ops.TensorOps method)

Z

zeros() (hpfracc.ml.tensor_ops.TensorOps method)

zeros_like() (hpfracc.ml.tensor_ops.TensorOps method)